Marine Protected Areas (MPAs) are increasingly established globally as a spatial management tool to aid in conservation and fisheries management objectives. Assessing whether MPAs are having the desired effects on populations requires effective monitoring programs. A cornerstone of an effective monitoring program is an assessment of the statistical power of sampling designs to detect changes when they occur. We present a novel approach to power assessment that combines spatial point process models, integral projection models (IPMs) and sampling simulations to assess the power of different sample designs across a network of MPAs. We focus on the use of remotely operated vehicle (ROV) video cameras as the sampling method, though the results could be extended to other sampling methods. We use empirical data from baseline surveys of an example indicator fish species across three MPAs in California, USA as a case study. Spatial models simulated time series of spatial distributions across sites that accounted for the effects of environmental covariates, while IPMs simulated expected trends over time in abundances and sizes of fish. We tested the power of different levels of sampling effort (i.e., the number of 500-m ROV transects) and temporal replication (every 1-3 yr) to detect expected post-MPA changes in fish abundance and biomass. We found that changes in biomass are detectable earlier than changes in abundance. We also found that detectability of MPA effects was higher in sites with higher initial densities. Increasing the sampling effort had a greater effect than increasing sampling frequency on the time taken to achieve high power. High power was best achieved by combining data from multiple sites. Our approach provides a powerful tool to explore the interaction between sampling effort, spatial distributions, population dynamics, and metrics for detecting change in previously fished populations.